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Algebra Level 4

Solve for real \(x,y,z : \) \[ \left\{ \begin{array}{l} \log_2 x+\log_4 y+\log_4 z=2 \\ \log_3 y+\log_9 z+\log_9 x=2 \\ \log_4 z+\log_{16} x+\log_{16} y=2 \\ \end{array} \right.\] Note: If \(x=\frac{a}{b} , y=\frac{c}{d} , z=\frac{e}{f} \), and (a,b) ; (c,d) ; (e;f) are coprime pairs of positive integers, then give a+b+c+d+e+f as the answer.

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